JERSEY CITY — State Sen. Sandra B. Cunningham is not running for mayor of Jersey City . . . or is she?

Cunningham has never explicitly denied she wanted the job, but when she announced in January that she would seek re-election to her Senate seat this year, that seemed to close the door on any entry into the mayor’s race.

But signs have been popping up in Jersey City calling Cunningham “the people’s choice” for mayor.

Cunningham is the widow of the late mayor Glenn D. Cunningham.

“She can’t be bought,” reads one of the signs, noted by a reader of The Jersey Journal.

Appearing in Jersey City Monday at an event with Gov. Chris Christie, Cunningham said she has seen the signs. Asked whether she was responsible for them, she replied, “No.”

If Cunningham wanted to jump into the race, she still has time, though she’d have to collect 1,331 valid signatures of registered city voters and submit them by 4 p.m. Monday.